In the Haber process, ammonia is synthesized from N2 and H2. Given the reaction N2 (g) + 3 H2 (g) ⇌ 2 NH3 (g) and ΔG° at 298 K is –33.3 kJ/mol, what is the value of ΔG at 298 K for a reaction mixture with partial pressures of 1.9 atm N2, 1.6 atm H2, and 0.65 atm NH3?
A
-15.0 kJ/mol
B
-40.5 kJ/mol
C
-25.7 kJ/mol
D
-33.3 kJ/mol
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1
Start by understanding the relationship between ΔG° and ΔG. The equation to use is ΔG = ΔG° + RT ln(Q), where R is the universal gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and Q is the reaction quotient.
Calculate the reaction quotient Q using the partial pressures given. The expression for Q is Q = (P_NH3)^2 / (P_N2 * (P_H2)^3), where P_NH3, P_N2, and P_H2 are the partial pressures of NH3, N2, and H2 respectively.
Substitute the given partial pressures into the expression for Q: Q = (0.65)^2 / (1.9 * (1.6)^3).
Convert the temperature to Kelvin if necessary, but in this case, it is already given as 298 K. Use the value of R in kJ/mol·K for consistency with ΔG° units: R = 0.008314 kJ/mol·K.
Substitute ΔG°, R, T, and Q into the equation ΔG = ΔG° + RT ln(Q) to find the value of ΔG at 298 K for the given reaction mixture.